microsoft reporting services qr code CHAP. 41 in Software

Creation QR in Software CHAP. 41

CHAP. 41
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FUNCTIONS
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The resulting output is the same as in Example 4.9.
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4.15 The combination function C(n,k) gives the number of different (unordered) k-element subsets
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that can be found in a given set of ~2 elements. The function can be computed from the formula
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C(n, k) = n! k! (n-k) !
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Imp lement this formula.
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This is a straightforward implementation of the formula: int comb(int, int);
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main0 -t for (int i = -1; i < 8; i++ > -c for (int j = -1; j <= i +l; j++) tout << " ' -CC comb <iA>; tout CC endl; 1 1 int factorial(int); // Returns C(n,k), the number of combinations of k from n: int comb(int n, int k)
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if (n c 0 II k c 0 II k > n) return 0; return factorial(n)/(factorial(k)*factorial(n-k));
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Notethatthe factorial0 function must be declared above the comb ( ) function because it function because it is is used by that function. But it does not need to be declared above the main ( > not used there.
FUNCTIONS
[CHAP. 4
4.16 Write and test the dig i t ( ) function: int digit(int n, int k)
This function returns the kth digit of the positive integer n. For example, if n is the integer 29,415, then the call digit (n, 0 ) would return the digit 5, and the call dig i t ( n , 2 > would return the digit 4. Note that the digits are numbered from right to left beginning with the zeroth digit.
This removes the right-most digit of n k times. This reduces n to an integer whose right-most digit is the same as the kth digit of the original integer. That digit is then obtained as the remainder from division by 10: int digit(int, int); main0 1 int n, k; tout << "Integer: "; tin >> n; do 1 tout << "Digit: "; tin >> k; tout << "The ' << k C-C "th digit of ' -CC n << ' is ' << digit(n, k) << endl; } while (k > 0);
// Returns the kth digit of the integer n: int digit(int n, int k) for (int i = 0; i < k; i++) // remove right-most digit n /= 10; return n % 10;
This run was on a computer whose in ts
can hold 9-digit integers.
4.17 The ancient Greeks classified numbers geometrically. For example, a number was called trian-
gular if that number of pebbles could be arranged in a symmetric triangle. The first eight triangular numbers are 1, 3,6, 10, 15,21,28, and 36:
T,= 1
T, = 3
T, = 6
T,= 10
T,= 15
CHAP. 41
FUNCTIONS
Write and test the boolean function:
int isTriangular(int n)
This function returns 1 if the given integer n is a triangular number, and 0 otherwise.
The argument n is triangular if and only if it is a sum of consecutive integers 1 + 2 + 3 + . So we just have to compute these sums until we find one that is greater than or equal to n. If that sum is equal to n, then n is a triangular number; otherwise, it isn t:
l l l
int isTriangular(int); main0 int n; do -t tin >> n; if (isTriangular( tout -CC n << ' is triangular.\n"; else tout CC n << ' is not triangular.\n"; } while (n > 0);
// Returns 1 i f n i s a triangular int isTriangular(int n) 1 int i = 0, sum = 0; while (sum < n) sum += ++i ; if (sum == n) return 1; else return 0;
number (1,
10, 15, etc.):
4.18 Write a maximum function for three integers that uses the maximum for two integers.
We assume that the max ( int , int max(int, int); in t ) function is already available:
int max(int x, int y, int z) -t int max(int,int); return max(max(x,y),z); )
FUNCTIONS
[CHAP. 4
4.19 Write a function that converts rectangular coordinates to polar coordinates.
Every point in the coordinate plane has a unique pair (x, y) of rectangular coordinates and a unique pair (r, 0) of polar coordinates with r 2 0 and 0 5 0 < 27~. The following function converts from rectangular to polar coordinates. Since the output consists of more than one variable, the two output variables r and t are passed by reference:
void rectangularToPolar(double&
r, double& t, double x, double y)
const double pi = 3.1415926535897932385; r = sqrt(x*x + y*y); if (x > 0) if (y >= 0) t = atan(y/x); else t = atan(y/x) + 2*pi; else if (x == 0) if (y > 0) t = pi/2; else if (y == 0) t = 0;. else t = 3*pi/2; else t = atan(y/x) + pi;
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